Optimal control of digital systems via discrete Legendre polynomials

Abstract

The shift transformation matrix for discrete Legendre polynomials is introduced in this study, and modified discrete Euler-Lagrange equations are constructed using the discrete variational principle combined with the idea of a penalty function. The discrete Legendre series are then applied to simplify the modified equations into a set of linear algebraic ones for the approximations of state and control variables of digital systems. An example is given to demonstrate this technique, when it is seen that this new method is straightforward and simple, giving a considerable saving in computing time.